In this work, the cooperation problem between two populations in a periodically varying environment is discussed. In particular, the two‐population prisoner's dilemma game with periodically oscillating payoffs is discussed, such that the time‐average of these oscillations over the period of environmental variations vanishes. The possible overlaps of these oscillations generate completely new dynamical effects that drastically change the phase space structure of the two‐population evolutionary dynamics. Due to these effects, the emergence of some level of cooperators in both populations is possible under certain conditions on the environmental variations. In the domain of stable coexistence the dynamics of cooperators in each population form stable cycles. Thus, the cooperators in each population promote the existence of cooperators in the other population. However, the survival of cooperators in both populations is not guaranteed by a large initial fraction of them.

中文翻译：

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是否在可预测但周期性变化的情况下合作？快速振荡环境中的合作

在这项工作中，讨论了在周期性变化的环境中两个种群之间的合作问题。特别是，讨论了具有周期性波动回报的两口囚徒困境游戏，这样在环境变化期间这些振荡的时间平均就消失了。这些振荡的可能重叠会产生全新的动力学效应，从而彻底改变两种群进化动力学的相空间结构。由于这些影响，在一定条件下因环境变化而在两个种群中都可能出现某种程度的合作者。在稳定共存的领域中，每个人口中合作者的动态形成稳定的周期。从而，每个人口中的合作者促进了其他人口中合作者的存在。但是，这两个群体中最初大部分人都无法保证合作者的生存。